33 citations · 106 across the 19 of their papers we have counts for
12 papers · 1 filter
Complexity Analysis of Root Clustering for a Complex Polynomial
Ruben Becker, Michael Sagraloff, Vikram Sharma +2
Let be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural -clusters of roots of in some box reg…
Counting Solutions of a Polynomial System Locally and Exactly
Ruben Becker, Michael Sagraloff
We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdot…
Efficiently Computing Real Roots of Sparse Polynomials
Gorav Jindal, Michael Sagraloff
We propose an efficient algorithm to compute the real roots of a sparse polynomial having non-zero real-valued coefficients. It is assumed that arbitrarily…
On the Complexity of Solving Zero-Dimensional Polynomial Systems via Projection
Cornelius Brand, Michael Sagraloff
Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we propose a certified and complete method to compute all complex solutions of the sy…
On the Complexity of Computing with Planar Algebraic Curves
Alexander Kobel, Michael Sagraloff
In this paper, we give improved bounds for the computational complexity of computing with planar algebraic curves. More specifically, for arbitrary coprime polynomials , $g \in…
Computing Real Roots of Real Polynomials
Michael Sagraloff, Kurt Mehlhorn
Computing the roots of a univariate polynomial is a fundamental and long-studied problem of computational algebra with applications in mathematics, engineering, computer science, a…